p:=◯;;n:=◯;;order:=p n;; # Input the values of p and n, where the order of G is p n | G:=AllSmallGroups(Size,order);; | D:=NumberSmallGroups(order);; | for k in [1..D] do; | f:=G[k];;m:=Size(MinimalGeneratingSet(f));;WW:=[ ];; | if NilpotencyClassOfGroup(f)=2 and m=2 then; | Add(WW,[1,1]); | Print(k,") G=",StructureDescription(f), " |G|=",Size(f)," p=",p,"n=",n," N.class | ",NilpotencyClassOfGroup(f)); | gg:=MinimalGeneratingSet(f);; | e:=Identity(f);; | a:=gg[1];;b:=gg[2];; | i:=Log(Order(a),p);;j:=Log(Order(b),p);;w:=Maximum(i,j);; | if i+j=n then; | m1:=1; m2:=p n/p w-1;Add(WW,[p,m1*p 2-1]); | if w>=2 then; | Add(WW,[p 2,m2*p 2]); | fi; | else; | m1:=p;m2:=p (n-w)-p;Add(WW,[p,m1*p 2-1]); | if w>=2 then; | Add(WW,[p 2,m2*p 2]); | fi; | fi; | Yw:=p (n-1)*(p-1);; | for 1 in [0..(w-3)] do; | Add(WW,[p (w-l),Yw/(p 1)]); | od; | Print("∖n no. of gen.=",m,", o(a)=",p i,", o(b)=",p j,", w=",w,"∖n OC=",WW,"∖n∖n"); | fi;od;time; |
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